Find the area of the triangle whose vertices are $(2, 3), (-1, 0),$ and $(2, -4)$.

Name the type of quadrilateral formed,if any,by the following points,and give reasons for your answer: $(-1,-2), (1,0), (-1,2), (-3,0)$.

If $Q(0, 1)$ is equidistant from $P(5, -3)$ and $R(x, 6)$,find the values of $x$. Also,find the distances $QR$ and $PR$.

Find the distance between the following pairs of points: $(-5, 7)$ and $(-1, 3)$. (in $\sqrt{2}$)

The Class $X$ students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of $1\, m$ from each other. There is a triangular grassy lawn in the plot as shown in the Figure. The students are to sow seeds of flowering plants on the remaining area of the plot.
What will be the coordinates of the vertices of $\Delta PQR$ if $C$ is the origin?
Also,calculate the area of the triangle in this case.

Find the centre of a circle passing through the points $(6, -6), (3, -7)$ and $(3, 3)$.